MCDEVIT-LONG EQUATION FOR SALTEFFECTS OR'
June, 1963
as large. That is, t,he bromide ion affects a volume about ten times its own in tlie flow process. The discrepancy between TV aiid 1 * ~thus supports our suggestion of electrostriction. The lion-electrolytic solutes also show evidence of electrostatic interaction with the solvent. The nonpolar or slightly polar solutes give B-values which are considerably smaller than one would expect from tlie corresponding volumes. The sequence of the last three compounds of Table I11 is especially informative; the three molecules have roughly the same shape and size, so the geometrical contributions to B should be not greatly different. The p-values, however, increase by nearly an order of magnitude in the sequence MeC6HJle, 02SCsH4S02, 02SCaH4n"2. The first two components have zero dipole moments, the first due to absence of electrical asymmetry and the second by compensation of vectorially opposed moments. The value of B for the diiiitro compound is, however,
Y OX-ELECTROLYTES L
1347
over four times that for p-xylene; strong local interaction between the individual nitro-dipoles and solvent molecules is clearly indicated. The value for p-iiitroaniline neatly confirms the argument; the net dipole moment is very large ( = 7 Debyes) and has an intense field at both ends. The value of B (2.94) is greater than the ideal 2.5, which shows the strong dipoles can also produce electrostriction in their vicinity. Finally, a comparison of tributylammonium picrate with tributylamine and picric acid also leads to the conclusion that electrostatic interaction, in addition to purely geometrical. effects, determines viscosity. The sum of V's for picric acid and the amine is 0.37, which is in fair agreement with 0.34, the value of V for the amine picrate. But the sum of the B's is only 0.64 as compared with 0.99 for the amine picrate. The field a t the nitrogen end of the Bu&H+ ion is of course much stronger than that a t the Bu3N nitrogen, and a large B is expected and found for the amine picrate.
THE: MCDEVIT-LONG EQCATIOK FOR SALT EFFECTS ON SON-ELECTROLYTES1 BY K. C. DENO, ~ N DCHARLESH. SPIKK~ College of Chemist?y and Physics, the Pennsyltanaa State Universaty, Universrty Park, Penna. Receaved January 31, 1963 Evidence is presented supporting the theory that the salting-out and salting-in of non-electrolytes depends on the molecular volume of solute and on the changes in internal pressure of the solvent which take place on addit,ion of salt.
The familiar salting-in or salting-out of non-electrolytes is correlated by the equation log f = kscs (1) where j' is the activity coefficieiit of the noli-electrolyte, lis is the Setschenow constant, and c, is the concentra,tion of salt in rn~les/liter.~ Based on the concept of volume energies, Long and RIcDevit4 derived the equation IC, =
vlyvs-
I',")/2.3RT@o
(2) Equation 2 requires that salt effects are determined by the molecular volume of the solute molecule and the extent of electrostriction, (V, - T:), of the solvent by the salt. Long aiid XcDevit used the compressibility data of Gibson5 t o evaluate the electrostriction. The resulting evaluation of k, for salt effect on the solubility of benzene in water ga,ve the correct salt order and correct sign of k , for a variety of salts. The concept of volume energies also has been used to correlate solubility and distribution data for a large number of hydrocarbons in mater,6 sulfur dioxide,{ and ammonia.' In these systems, the activity coefficient of the non-electrolyte is again related to the volume energies (1) This q o i k was supported in p a r t b y t h e Petroleum Research Fund administered by t h e American Chemical Society. Grateful acknovledgment is hereby made of this support. (2) Recipient of a d u Pont Fellomship. (3) F. A Long and T. F. AfcDe\it, Chem. Rev.,61, 119 (1952). (4) I-. A Lona and W. F. hIcI)e\,it, J . A m Chem. Soc., 74, 1773 (1952). (5) R. E. Gibson, zbsd., 66, 4, 865 (1934); 67, 284 (1935). (6) J. C. McGowan, J . A p p l . Chem., 2, 323 (19521, 4, 41 (1954). (7) N. Deno a n d H. Berkbeimer, J . Chem. Eng. Data. 4, 1 (1959).
RT In f
=
VAP,
(3)
In eq. 3, V is the molecular volume of the solute arid A p e is an empirical parameter that depends only on the two liquid phases and js iiiterpret,ed to be the difference in internal pressures.* If eq. 3 is differentiated with respect to salt concentration for solutions of non-electrolyt'es in varying salt concentrations, eq. 4 results. d logf/'dc,
=
k,
=
(V/2.3RT)(dAPe/dcS)
(4) Since V is approximately equal to Vifl for non-electrolytes, eq. 2 and 4 are equivalent. The change in iiiternal pressure with salt concentration, d APe/dcs in eq. 4,is equal to the internal pressure factor, ( V , - Vi0)JPD,, +sf the McDevit-Long eq. The success of eq. 3, independent of eq. 2, supports the McDevit-Long eq. (eq. 2 ) and suggests that eq. 2 or 4 deserves more experimentaJ testing than has previously been given. 3 * 4 , 9 Experimental The solubilities of tetralin, diphenylmethane, and 2,4-dipheny.l2-methyl-2-pentene were measured in sodium sulfate solutionn. Concentrat)ions of the hydrocarbons in solution were determinesd by conventional spectrophotometric methods using a Beckman DU spectrophotometer. All hydrocarbons were distilled and., ( 8 ) The original notation of McGowan (ref. 6 a n d 7) has been changed in order t o be more consistent with t h e underlying concepts a n d with t h e noteltions of Gibson (ref. 5 ) a n d Long a n d 'lcDevit (ref. 4). T h e original expression of McGowan was (log f = k k l f ' ) , where k~ is a constant for a given solvent pair a n d P is t h e Parechor, a measure of molecular volume. AfcGowan's expression f o r t h e molecular volume near t h e m.p., 0.42 P (J. C. bloGowan, Rec. trav. chim., 76, 199 (1956)), is t h e most convenient way t o estimate V in eq. 3 in view of t h e availability of Tables of Paiaclior increments (0. R. Quayle, Chem. Reo., 63,484 (1958)). (9) XI. A. Paul, J . Am. ('hem. Soc., 74, 5274 (1952).
S. C. DESO AND CHARLESH. SPINK prior to each experiment, chromatographed through activated alumina. The general procedure was to mix about 0.5 ml. of hydrocarbon with 30 rnl. of salt solution in glass stoppered flasks and to allow the samples to equilibrate with gentle agitation a t 25'. Aliquots were withdrawn from the aqueous phase intermittently for spectral measurement. When the optical densities were constant within ZY,, equilibration was regarded as complete. Spectral measurements were made a t a number of wave lengths for each compound in order to check for possible oxidation and colloidal dispersion. Beer's law tests were made on each hydrocarbon. The sodium sulfate was analyzed for water content by ignition. The salt solutions were checked for optical purity in the ranges where measurements were made. The solubilities of the above hydrocarbons were also determined in aqueous tetramethylammonium bromide solutions. I n the wave length region 230 to 250 mp, there was a 10-7 absorption which increased slowly with time. For the tetralin and diphenylmethane experiments this absorption was not significant. As a precaution, however, fresh salt solutions were prepared immediately before use.
Discussion The Setschenow constants were determined from eq. 1. The data in Table I demonstrate that the proportionality between molecular volume and k,, required by eq. 2, is exhibited for both salting-out and salting-in. The deviation for molecules of small volumes such as ethylene arises from occupation of interstitial space as explained for similar deviations from eq. 3.' T.4BLE
1
CORRELATIOK OF THE SETSCHENOW COSSTANT ( k , ) WITH MOLECULAR VOLUME FOR SapS04AND (CH3)& +Br- SOLUTIOXS V5 W./ Non-electrolyte
mole)
Ethylene 42 Benzene 86 Naphthalene 131 1,2,3,4,-Tetrahydronaphthalene 139 Biphenyl 160 Diphenylmethane 177 2,4-Diphenyl-X-methyl2-pentene 251 Estimated as suggested in physik. Chem., 40, 535 (1902).
Na%soa
k,
0.42* .54" .72d
.74 .88
ks/ T' X 103
(CHaIrN +Brk d' J kB X 108
10 6 . 3 -0.15 5.5
-1.8
5 . 3 - .28 - 2 . 0 5.3 5.0 - .37 - 2 . 1
Vol. 67
R4N+Br- salt's mere measured in this work and are reported in Table 111. TABLE I1 EXPTL.VALUES O F k s
COMP.4RISOX O F CALCD. A N D
(0.3k,)a (calcd. from
-
Salt
V S -
The relatively small drift in ks/V values in Table I may be due to the Kirkwood interaction term, ro/(rc r,), which was proposed as a possible additional factor for eq. Z 3 In this term, ro is the radius of the cation in solution and rn is the radius of the non-electrolyte.1° The radii are unambiguous for spherical molecules, but in more complex molecules, such as those approachiiig cylindrical shapes, T, is more nearly approximated by the radius of a cross section of the cylinder. Thus 7-n does not necessarily continue to increase with increasing molecular volume. The term, ( V , - v2)/2.3RTPo,has also been tested beyond the initial considerations of Long and McDevit.3 Table I1 summarizes the test and again a reasonable fit is found for both salting-out and salting-in. For V,, the volume of the salt in solution, the formulations of Mukerjeell were used. I n the case of the large tetraalkylammonium salts, where Xukerjee's method is not applicable, V s was estimated by the relation, T i = 0.42P, where P is the Parachor.8 The values for the
7% (exptl.]b
TABLE I11 DEXSITIESO F -4QUEOUS SALT SOLUTIOXS AT 25" Salt
Wt. %
Density, g./ml.
(CHghNBr
0.00 3.95 6.00 7.97
0.9971 1.0074 1.0122 1.0186
V.0
=
vBO=
( CHaCHsCHp)aNBr
+
(10) J . G. Kirkwood, Chem. Rev., 24,233 (1939). (11) P. Mukeriee, J . Phvs. Chem., 65, 740,744 (1961).
eq. 2)
BEKZENE
214 2.5 Al,(SO,), 1.2 Na?S04 53 0.58 0.55 BaClz 41 .47 .33 NaOH 22.3 .26 .26 NaF 18.6 .21 .25 XaC1 12.8 .16 .20 KCl 10.3 ,12 .17 KaBr 13.6 .14 .l G LiCl 10.4 .12 .14 9.0 .10 RbCl .14 KBr 10.1 .12 .12 r\"aC1 9.0 .10 .10 CsC1 8.7 .10 .09 CaHjCOSa - 4.4 - .05 - ,05 C6H&hxa - 9.0 - .10 - .09 - .15 -10.0 - .ll (CH&NBr - .26 - .25 (CpH&SBr - 23 - .37 - .41 - 32 ( C3H,)4SBr a The 0.3 factor is an arbitrary factor introduced to improve the agreement. It is evident that eq. 2 in its present form is more successful in calculating relative values for k, rather than absolute values. In using eq. 2, t.he compressibility of water, P O , was taken as 39.6 X 10-6 bar-' and the molar volume of benzene, BiO, was taken as 86 ml./mole. Most of the values are from ref. 3 and 4.
( CH3CH2)4NBr
1.05 4.2 footnote 8. J. Billitzer, 2. Ref. 3. Ref. 9.
Van
FOR
112.1 ml./mole 4.15 6.11 8.15 170.3 ml./mole 4.07 6.11 8.09
1.00480 1.00861 1.01270 1,00282 1.00502 1.00831
-
Vso = 225.8 ml./mole
The only major deviation is for h l ~ ( S 0 4 ) ~This . salt differs from the others in Table I1 in that one of the ions, Al+3, is strongly bonded to water by covalent bonds.12 It would be more proper to regard the ion as AI(H20)s+3. The formation of covalent bonds lowers the value of v2 beyond the electrostriction effect so that ( V , - l72)and k, calculated by eq. 2 are too large. The tests of eq. 2 can be extended to include polar molecules. Equation 3 has been extended to include solutes which specifically bond to solvent (5)"7 RT ln f = VAP, 4- A F H Since such bondiiigs are usually hydrogen bonds, the symbol A F H was used. It was found that A F s was characteristic of the type of functional group and exactly proportional to the number of such (12) H. Taube, zbzd., 58, 523 (1954).
KIKETICS OF COALCOMBUSTION
June, 1963
1349
If eq. 5 is differentiated in respect to salt concentration, eq. 6 results. This equation predicts that the Setsche-
now constant for a solute that is hydrogen bonded to sohent depends on the rate of change of AFH with salt concentration, as well as the internal pressure changes. RT (d In f / d c s ) = V(d APe/dcs) d AFE/dcs (6) For some solutes, such as those shown in the upper part of Table IV, k s / V is the same as for benzene, from TABLE IV which it is concluded that d AFH/dc, is zero. For many solutes, d AFH/dcs is not zero. PresuniVALUESOF ks/V FOR POLAR SOLUTES COMPARED TO BEKZEXE (NH&SOa AS THE SALT (25') USING: ably, direct interaction between solute and the ions of V ha/ v the added salt occurs. Long and Bergen have listed (ml./mole)b x 10% kaa Solute k, values for a number of polar solutes, principally 86 4.6 0.396' Benzene amines and carboxylic acids.13 These data have been ex3.6 .154 42 Methanol amined in detail.14 I n 41 out of 57 examples, the value 59 4.0 Ethanol ,249 of k,/V was within 50yoof the value for benzene so that 1-Propanol ,336 76 4.5 even here the internal pressure effect accounts for the 1-Butanol .417 93 4.3 major part of the salt effect. The values of d AFH/dc, 2-Butanol .40 91 4.5 that were largest in magnitude were found for carboxDiethyl ether .42 89 4.8 ylic acids (RCOOH) with salts of the alkali metal ions. 1,2-Dimethoxyethane .37 97 3.8 The values were negative as expected for a significant Diisopropyl ether .54 119 4.5 interaction between RCOOH and the alkali metal ion. Dipropyl ether .62 122 5.0 Other metal ions would presumably exhibit even more Acetone .30 66 4.5 negative values, but data are not available. SignifiCyclohexanone .42 108 3.8 cantly, d AFH/dc, for carboxylic acids was zero when Propionaldehyde .26 67 3.8 tetraalkylaminoniuin salts were added. X o interaction Butyraldehyde .42 84 5.0 between carboxylic acid and cation would be expected 2,3-Butanedione .98 86 14.1 in these cases and this demonstrates that there is nothFormaldehyde - .02 34 -0.6 ing abnormal about the carboxylic acids in general. Acetaldehyde I14 50 2.8
+
a W. Rieman, 111,J . Chem. Educ., 38,338 (1961), unless noted. Calculated by the method used in Table 11. Footnote 8.
(13) F. A. Long and R. L. Bergen, J . Phys. Chem., 60, 1131 (1956). (14) Ph. D. Thesis of Charles H. Spink, Pennsylvania State Univ., 1962
KINETICS OF COAL COMBUSTIOK: THE IYFLUEXCE OF OXYGEX CONCENTRATIOS O S THE BURNISG-OUT TIMES OF SISGLE PARTICLES BY GEOFFREY BEESTOK Department of Fuel 2'echnology and Chemzcal Engineerzng, Cnuerstty of Shefield, England AND
ROBERTH. ESSENHIGH
Department of Fuel Technology, College of Mineral Industries, The Pennsylvanta State Einzversaty, Universzty Park, Pa. Received Kovember g4, 1966 The combustion behavior of captive particles from a single coal, in the size range 2 mm. down to 350 p , has been studied as a function of oxygen vitiation and enrichment; this supplement8 previous work on a range of coals of volatile matter 5-40y0, designed to study the influence of rank, but which1 were burned only in air. I n these present studies, particles of 5 different diameters were burned in quiescent oxygen atmospheres ( P O )ranging from 3 to 70%, a t an approximately constant temperature of about 1000"; and their burn-out times (tb) were measured with a stopwitch. The results agreed very well with theory, which predicted that tb was inversely proportional to In (1 - pa), thus implying that the reaction with respect to p a t the solid surface is first order. The theory used was a modification of the Nusselt diffusion-film hypothesis of reaction control. The original theory was restricted to the condition that po was small, in which case t b is proportional to pa, the first term of the logarithmic expansion; but with the wide range in oxygen concentration used in these experiments, the use of the full logarithmic expression was found to be necessary. From the theory, the value of the constant of proportionality could also be calculated from first principles, and this calculated value mas found (fortuitously but acceptably) to be in exact agreement with the experimental value.
1. Introduction Single particles of coal burn in t J T 0 stages. The first is a volatile combustion stage and the second. rvith which this paper is primarily concerned, is burn: out of the solid carboll residue left after generation and combustion of the Trolatiles. Kinetically, this second, burn-out stage is a heterogeneous process in which oxygen reacts directly, at-and-with the solid surface. It has, therefore, been studied extensively, but as it were by proxy using relatively pure carboll in place of the coal; and the validity of extrapolating such results
-
directly to coal residues has generally been then taken very much for granted. Direct work on coal has, 01 course, been done in the past but the r e ~ u l t s l -have ~ generally been too few, and the conditions too imprecise, for kinetic studies. Further experiments have, therefore, been carried out on single particles of coal under (1) H. K. Griffin, J. R. Adams, and D. F. Smith, Ind. Eng. Chen., 21, 808 (1929). (2) A . L. Godbert, Fuel, 9 , 57 (1930); -4. L. Godbert and R. V. Wheeler, "Safety in Mines Research Board," Paper KO.73 H.X.S.O., London, 1932. (3) A. A. Orning, Trans. A S M E , 64, 497 (1942); T. J. Omori and A. A. Orning, %bza.,ra, 591 (1950).
